Answer
a) The equations of tangent lines are:
$y=\frac{-3x}{4}+\frac{25}{2}$
$y=\frac{3x}{4}-\frac{25}{2}$
b) see the graph
Work Step by Step
The equation of the circle is $x^2+y^2=100$.
At $x=6$, $y=\pm 8$
The equation of a line passing through a given point $(x_0,y_0)$ is given by
$y-y_0=m(x-x_0)$ where $m$ is the slope of the line.
Slope of the tangent $m=\frac{dy}{dx}$.
Differentiating $x^2+y^2=100$ we get $\frac{dy}{dx}=\frac{-x}{y}$.
The equation of the tangent line passing through the point$(6,8)$ is,
$y-8=\frac{-6}{8}(x-6)$
Simplifying we get, $y=\frac{-3x}{4}+\frac{25}{2}$
The equation of the tangent line passing through the point$(6,-8)$ is,
$y-(-8)=\frac{-6}{-8}(x-6)$
Simplifying we get, $y=\frac{3x}{4}-\frac{25}{2}$
